Ahrefs or Majestic

Always Ahrefs > Majestic

Go for ahrefs always. Their database and server power outweighs any kind of benefit majestic may have over it.

Btw, ahrefs and majestic are individual organizations which has their own algo, crawling speed and metric value calculations and its limitations, so you can not expect the same results on both ahrefs and majestic or even moz as well... I could say both has their own values...so personally i wont prefer over other, but ahrefs i can recommend you!